1. Andrea Meld, PhD Assessment Analyst, OSPI andrea.meld@k12.wa.us

2. Description of Statewide Sample: A cohort of 43,754 students tested in both Reading and Math WASL who were : Grade 4 students in Spring 2000 Grade 7 students in Spring 2003, and Grade 10 students in Spring 2006 51% female, 49% male 2% Native American, 4% African American 8% Asian, 9% Hispanic and 77% White. This sample may be different in some ways from Washington state students as a whole because a cohort (by definition) does not contain students whose families are mobile.

3. Descriptive Statistics for Reading and Math WASL Grade 4, 7 and 10 Cohort ReadingMinMaxMedMeanSD Grade 4311478410410.218.80 Grade 7314470402400.517.93 Grade 10291525437436.232.18 MathMinMaxMedMeanSD Grade 4190519399396.933.19 Grade 7168624394393.650.23 Grade 10228575407406.135.62

6. Pearson Correlations Statewide Cohort WASL Reading Scale Scores WASL Math Scale Scores Grade 7Grade 10 Grade 4.649.569 Grade 7.637 Grade 7Grade 10 Grade 4.745.694 Grade 7.778

7. Statewide Cohort Questions, Comments, Interpretation of Data

8. Thought experiment You’re a teacher at Emerald Elementary in the Green School District. 100 students in your school take the WASL in 2000 as 4 th graders. Imagine them lined up in order of their WASL Reading Scores and then again in the order of their WASL Math, Students who receive the same rank stand side by side. Now, do your two lines look the same? Are the students in the same order?

9. Thought experiment continued Jump ahead to 2003. You now teach at Sage Middle School. These same 100 students now attend Sage as 7 Th grade students and take the Reading and Math WASL. Again, imagine the students lining up in rank order of WASL Reading and WASL Math scores. You see familiar faces, but are these students in the same order as they were in grade 4?

10. Thought experiment continued It’s now 2006, and you are now the District Assessment Coordinator for Emerald SD. The WASL is a major part of your work. You would like to know to what extent is the rank order of the students in the 2000-2003-2006 cohort the same as in previous WASL Reading and Math Assessments.

11. Correlations among rank-ordered variables WASL Reading RankWASL Math Rank Grade 7Grade 10 Grade 4.757.702 Grade 7.790 Grade 7Grade 10 Grade 4.733.692 Grade 7.801

12. Math Rank Grade 4 by Grade 10 Reading Rank Grade 4 by Grade 10

13. Questions, Observations, Comments?

14. Appendix – SPSS Syntax to Create Rank Variables and Spearman vs. Pearson SPSS Syntax Rank RANK order (1=highest value and 100 is lowest value) VARIABLES=rscale6 (A) /RANK /PRINT=YES /TIES=MEAN. Percentile AKA Fractional Rank RANK percentile (100=highest value and l is lowest value) VARIABLES=rscale6 (A) /RFRACTION /PRINT=YES /TIES=MEAN.

15. Pearson vs. Spearman Syntax for Pearson correlation -- r Use when you have equal interval scale, measures are the same or equivalent. Large sample or population Magnitude of association is important CORRELATIONS /VARIABLES=mtraw6 sscale6 /PRINT=TWOTAIL NOSIG /MISSING=PAIRWISE. Syntax for Spearman correlation -- rho Use when you have ordinal scale, measures may be different. Good for survey data, e.g, Likert scales, agree/disagree Smaller sample or population (~ 100) Need to reject Null Hypothesis that two measures are not related. NONPAR CORR /VARIABLES=mtraw6 sscale6 /PRINT=SPEARMAN TWOTAIL NOSIG /MISSING=PAIRWISE. NOTE: Running Pearson correlation on ranked variables = Spearman correlation.

16. For more information on Spearman correlation http://www.google.com/search?hl=en&q=spearman+pearson&btnG=Google+Search http://www.google.com/search?hl=en&q=spearman+assumptions&btnG=Search http://www.google.com/search?hl=en&q=spearman+rank+order&btnG=Search http://www.google.com/search?hl=en&q=spearman+rho&btnG=Google+Search